How to find lines that intersect at least 3 different points on Y axes with 2 % error range?

I have time series data which consists of the time and closing prices of a stock. To automatically find trend (or trend like) lines I tried best fit - poly fit (polyfit(x,y,1)). As it is known, lines passing through 3 or more points are considered as trend lines financially and these points must be the lows or highs in the data set. So to be able to find local lows/highs IsChange() function which finds abrupt changes in data seems to be useful. The problem is that after finding local highs (or lows) how to find a line/lines that at least intersect 3 different points with max. 2% error range? Thanks.

Answer 1

[Abhaya]

Hi Mayya,

To find the trend lines that intersect at least 3 local highs or lows with a maximum 2% error, you can follow the steps given below.

• Identify Local Highs and Lows: First, you need to identify the local highs and lows in the dataset. Below is a sample code to find local highs in the ‘prices’ vector and store their indices in the ‘extrema’ vector:

        for i = 2:n-1
           if prices(i) > prices(i-1) && prices(i) > prices(i+1)
              extrema = [extrema, i];  % Local high
            end
        end

• Fit a Line Using Minimum number of Points: Select the minimum number of points required from the vector used to store highs(or lows) and fit a line using the corresponding x and y values from these points.

        pointsSubset = extrema(i:i+minPoints-1);
        xSubset = x(pointsSubset);
        pricesSubset = prices(pointsSubset);

• Fit a Linear Trend Line:Use the polyfit function with degree 1 to fit a straight line to the selected points:

        p = polyfit(x(points), y(points), 1);  

• Error Checking: Calculate the error between the fitted line and the actual data points.

        % Calculate the predicted values using the fitted line
        pricesPred = polyval(p, xSubset);
        
        % Calculate the error (percentage error) for each point in the subset
        errors = abs((pricesSubset - pricesPred) ./ pricesSubset) * 100;

If the maximum percentage error is less than 2% for all points on the trend line, store the line as a valid result.

        if all(errors <= maxError)
            % If error is within 2%, store the trend line if it passes 3 points
            trendLines{end+1} = struct('slope', p(1), 'intercept', p(2), 'points', pointsSubset);
        end

For a set of 20 random points, the result can be visualised as figure attached below.

Please refer to the following MATLAB documentation for 'polyfit' and 'polyval' functions.

• https://www.mathworks.com/help/matlab/ref/polyfit.html
• https://www.mathworks.com/help/matlab/ref/polyval.html

Hope this solves your query.